assume that 20% of criminal suspects who agree to take lie detector tests are actually guilty while 80% of those who agree to take the test are innocent. of those who are guilty, 70% fail the lie detector test. of those who are innocent, only 15% fail the test. suppose a person is arrested and takes a lie detector test. given that the person fails the test, what is the probability that the person is actually innocent?

The length of r in the right triangle is 14.01 metres.

A right triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the side r of the right triangle as follows:

using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

r² = 6.71² + 12.3²

r² = 45.0241 + 151.29

r = √196.3141

r = 14.0112133664

r = 14.01 metres

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If a driver travels at the speed of 40 mph, then the ratio of his speed in miles to minutes would be equal to 2/3 miles per minute.

The problem is based on simple conversion of units of speed from SI system to imperial system (it is named so because it was discovered in Britain). The speed of the driver is 40 mph that is 40 miles per hour. It means that to convert it into the ratio of miles and minutes, the relation between minutes to hours is to be known.

It is  known that one hour is equal to 60 minutes. Therefore speed of driver is calculated as 40/60 miles per minute, which is equal to 2/3 miles per minute.

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Answer:12/25=sind*cosd

3/5=sinc

4/5=sind

16/15=tand*cosc

Step-by-step explanation:

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To write the center and radius of a circle, we need to have the equation of the circle in standard form, which is: (x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius.

A circle is a geometrical figure that is defined as a closed shape where all the points on the boundary of the shape are at an equal distance from the center point. The center of a circle is the point which is equidistant from all points on the circumference of the circle. To determine the center of a circle, we need to follow some steps:

Step 1: Identify the coordinates of three points on the circle

To find the center of a circle, we need to know the coordinates of at least three points on the circumference of the circle. The coordinates of these points can be determined by measuring the distance of the points from the x-axis and y-axis.

Step 2: Find the perpendicular bisectors of two chords

Once we have identified three points on the circle, we need to find the perpendicular bisectors of two chords. A chord is a line segment that connects two points on the circumference of the circle. The perpendicular bisector of a chord is a line that is perpendicular to the chord and passes through the midpoint of the chord.

Step 3: The intersection of perpendicular bisectors is the center of the circle

The perpendicular bisectors of two chords will intersect at a single point. This point is the center of the circle. To verify that this point is indeed the center, we can measure the distance from the center point to the three points on the circle. If the distances are equal, then the point is indeed the center of the circle.

In summary, to find the center of a circle, we need to identify the coordinates of at least three points on the circumference of the circle, find the perpendicular bisectors of two chords, and then find the intersection of the two perpendicular bisectors. This point is the center of the circle.

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Answer:

123,000,000 as a multiple of a power of 10 is

1.23 x 10⁸ .

Answer:

21 boys

Step-by-step explanation:

girls 3+3=6+3=9+3=12+3=15+3=18+3=21

boys 2+2+2=6+2=8+2=10+2=12+2=14

3times 7=21

2 times 7 equals 14

so 21+14=35

The volume of the container is 91125 cubic meters.

What is volume?

A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

A sphere is the most basic and typical form of a three-dimensional shape. A sphere's radius is the simplest parameter to measure. The radius of the sphere is used to determine its volume.

Given the edge of a cube is 45 meters.

The formula of volume is V = s³.

The volume of the container is

45³

= 91125 cubic meter.

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Answer:

√1.5

Step-by-step explanation:

As a fraction, the square root of 3/2 can be expressed as √1.51 or just as √1.5.

A tangent line is a straight line that intersects a circle at only one point, and it is perpendicular to the radius that goes through that point.

Tangent lines are important because they help us determine the relationship between circles and other geometric shapes.
To find the tangent line to a circle, we need to first identify the point of intersection between the circle and the line.
A tangent line to a circle is a line that intersects the circle at exactly one point, called the point of tangency. The tangent line is perpendicular to the radius that intersects the point of tangency.

m = [tex]\frac{-1}{r}[/tex]

where m is the slope of the tangent line, and r is the radius of the circle.

The equation of a tangent line to a circle can be found using the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1, y1) is the point of tangency and m is the slope of the tangent line.

The length of the tangent segment from the point of tangency to the point of intersection with a secant line can be found using the formula:

[tex]t^2[/tex] = s1 * s2

where t is the length of the tangent segment, and s1 and s2 are the lengths of the two segments of the secant line that intersect the circle.
In terms of calculating the tangent line, we can use the point-slope formula.

Let's say we have a circle with equation [tex]x^2[/tex] + [tex]y^2[/tex] = [tex]r^2[/tex] and we want to find the tangent line at the point (a,b).

We can start by taking the derivative of the equation with respect to x, which gives us 2x + 2yy' = 0.

Solving for y', we get y' = -x/y.

Then, we substitute the values of x and y at the point of intersection (a,b) to get the slope of the radius at that point.

Finally, we take the negative reciprocal of that slope to get the slope of the tangent line, and use the point-slope formula to find the equation of the tangent line.
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Given that the square region has been partitioned into 5 identical rectangular regions, and the perimeter of each rectangular region is 30. We are to find the perimeter of the square region.

As we know that the perimeter of a rectangle is given by P= 2 (l + b)
Let's say the length of the rectangle is 'l' and the breadth of the rectangle is 'b'. Since the five rectangular regions are identical, all of them will have the same length and breadth. Let's take the length and breadth of each rectangular region as x and y respectively. So, the perimeter of each rectangular region is given by P = 2(x + y) = 30Given P = 30, we get2(x + y) = 302x + 2y = 30x + y = 15... equation (1)
We know that the square region is partitioned into 5 identical rectangular regions. Therefore, the length of the square region will be 5 times the length of the rectangular region and the breadth of the square region will be the same as the breadth of the rectangular region. So, length of the square region = 5x, and breadth of the square region = y.
The perimeter of the square region = 2(5x + y) = 10x + 2yAs we know that x + y = 15 (from equation 1)So, 10x + 2y = 10(x + y) + 8y= 10(15) + 8y= 150 + 8y. Therefore, the perimeter of the square region is 150 + 8y.

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The surface area of the cylinder with radius 5 inches and rectangle with height 4 inches is equal to 282.6 square inches.

Radius of the base = 5 inches

Height of the rectangle = 4 inches

Surface area of a cylinder

= area of the top and bottom circular faces + the area of the curved surface.

Here,

Rectangle represents the curved surface of the cylinder, with a height of 4 inches and a length equal to the circumference of the base.

Circumference of the base is equal to,

Circumference

= 2πr

= 2 x 3.14 x 5

= 31.4 inches (approx.)

Area of the curved surface of the cylinder is ,

Curved surface area

= Length x Height

= 31.4 inches x 4 inches

= 125.6 square inches

Area of each circular face of the cylinder is ,

Circular face area

= πr²

= 3.14 x 5²

= 78.5 square inches

Substitute the value to get total surface area of the cylinder we have,

Total surface area of the cylinder

= 2 x Circular face area + Curved surface area

= 2 x 78.5 square inches + 125.6 square inches

= 282.6 square inches (approx.)

Therefore, the surface area of the cylinder is approximately equal to 282.6 square inches.

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Based on the given information, the scout should choose Player A if they are looking for consistency.

What are range and standard deviation?

Range is the difference between the highest and lowest scores in the set.

Standard deviation measures how spread out the scores are from the mean.

To determine which player is more consistent, we need to look at the variability in their scores. One way to measure variability is to calculate the range and the standard deviation of each player's scores.

The smaller the range, the more consistent the player's scores are.

A smaller standard deviation indicates that the scores are closer together, which means the player is more consistent.

Using the data provided, we can calculate the range and standard deviation for both players:

Player A:

Range = 21 - 0 = 21

Standard deviation = 5.70

Player B:

Range = 48 - 3 = 45

Standard deviation = 10.89

From these calculations, we can see that Player A has a smaller range and a smaller standard deviation, which means that their scores are more consistent than Player B's. Therefore, the scout should choose Player A if they are looking for consistency.

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The polynomial that represents the area of the shaded region is 7x-1 ( optionA)

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares

Therefore, the area of the shaded region = area of the big rectangle - area of the small rectangle

area of the big rectangle = l×b

= (x-1)(x+5)

= x²+5x -x -5

= x²+4x-5

area of the small rectangle = l×b

=( x+1)(x-4)

= x²-4x+x-4

= x²-3x-4

therefore area of the shaded part

= x²+4x-5 - (x²-3x-4)

= x²+4x-5-x²+3x+4

collect like terms

x²-x²+4x +3x+4-5

= 7x -1

therefore the polynomial that represents the area of the shaded part is 7x-1

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The depth of water in a tank oscillates once every 6 hours, with a smallest depth of 5.5 feet and a largest depth of 8.5 feet. This can be expressed in a formula as a function of time in hours. The formula is: Depth = 5.5 + (3/2) * sin(2πt/6)

The formula is: Depth = 5.5 + (3/2) * sin(2πt/6), where t is the time in hours. This formula expresses the oscillating nature of the water level, which ranges from 5.5 to 8.5 feet. The sine function used in the formula reflects the oscillation of the depth. The frequency of the oscillation is determined by the factor (2πt/6) and the range is determined by the amplitude (3/2).
To better understand this formula, consider the example of a tank with a depth of 5.5 feet when the time is 0 hours. After 6 hours, the time has increased to t = 6 and the formula yields a depth of 8.5 feet. This shows that the formula is correctly representing the oscillation of the water level, with an amplitude of 3/2.

To summarize, the formula for the depth of water in a tank oscillating once every 6 hours with a smallest depth of 5.5 feet and a largest depth of 8.5 feet is given by the expression Depth = 5.5 + (3/2) * sin(2πt/6). This formula incorporates a sine function with a factor (2πt/6) and an amplitude of 3/2. The factor determines the frequency of the oscillation, while the amplitude determines the range of the oscillation.

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The two values that are in the solution set are -6 and 4, since both of these values satisfy at least one of the inequalities in the compound inequality.

What is inequality equation?

An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

To solve the compound inequality 4(x + 3) ≤ 0 or x + 1 > 3, we can first simplify the left-hand side of the first inequality:

4(x + 3) ≤ 0

4x + 12 ≤ 0

4x ≤ -12

x ≤ -3

Now we can solve the second inequality:

x + 1 > 3

x > 2

Therefore, the solution set for the compound inequality is all values of x that are less than or equal to -3 or greater than 2. This can be written in interval notation as:

(-∞, -3] ∪ (2, ∞)

Therefore, the two values that are in the solution set are -6 and 4, since both of these values satisfy at least one of the inequalities in the compound inequality.

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To balance the equation, the right side of the equation must also change by 4%.

What is equation?

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equals sign (=)

To balance the exchange equation, the percentage change on the left side of the equation [tex](\% \triangle M + \% \triangle V)[/tex] must equal the percentage change on the right side of the equation [tex](\% \triangle P + \% \triangle Q)[/tex].

Given that there has been a 3% change in the money supply [tex](\% \triangle M)[/tex] and a 1% change in velocity [tex](\% \triangle V)[/tex], the left side of the equation can be written as:

[tex]\%\triangle M + \%\triangle V = 3\% + 1\% = 4\%[/tex]

To balance the equation, the right side of the equation must also change by 4%. Therefore, the correct answer is:

B. 4%

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The double number line shows that Hiawatha is 75% as old as Itzel. This means that Hiawatha's age is 75% of Itzel's age. If we let Itzel's age be x, then Hiawatha's age is 0.75x.

A double number line is a visual representation of two related numerical quantities, such as distance and time or cost and quantity.

It consists of two parallel lines that are divided into equal segments or tick marks.

Each line represents one of the quantities, and the tick marks show the values or measurements of that quantity.

To complete the table showing different percentages of Itzel's age, you can choose different values of x and then calculate 75% of that value to find Hiawatha's age. For example:

If Itzel is 20 years old, then Hiawatha is 0.75 x 20 = 15 years old (since he is 75% as old as Itzel).

If Itzel is 40 years old, then Hiawatha is 0.75 x 40 = 30 years old.

If Itzel is 60 years old, then Hiawatha is 0.75 x 60 = 45 years old.

You can continue this pattern for different values of Itzel's age to complete the table.

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The double number line demonstrates that Itzel is 75% older than Hiawatha, who is 24 years old.

Itzel is 25% older than Hiawatha, who is 8 years old.

Itzel is 100% older than Hiawatha, who is 32 years old.

The visual representation of two linked numerical quantities, such as length and time or price and quantity, is called a double number line.

Two parallel lines that have been separated into equal pieces, or tick marks, make up the object.

The tick marks on each line denote the values or measurements of each quantity, and each line represents one of the quantities.

You can select various numbers of x and then multiply that number by 75% to determine Hiawatha's age in order to finish the table that displays various percentages of Itzel's age.

The double number line demonstrates that Itzel is 75% older than Hiawatha, who is 24 years old.

(24/3) = 8 => 25% of Itzel's age

(8*4) = 32 => 100% of Itzel's age

From the double number line

Age (years)     Percentage

[24]                 75% of Itzel's age

[ 8]                  25% of Itzel's age

[32]                 100% of Itzel's age

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The complete question is attached below,

To convert kilometers per liter to miles per gallon, we need to use conversion factors. There are approximately 3.785 liters in a gallon, and there are approximately 1.609 kilometers in a mile.

So, first we convert the fuel efficiency of the hybrid vehicle from kilometers per liter to kilometers per gallon:

1 km/liter * 3.785 liters/gallon = 3.785 km/gallon

Then, we convert kilometers per gallon to miles per gallon:

3.785 km/gallon * 1 mile/1.609 km = 2.35 miles/gallon

Therefore, the gas mileage of the hybrid vehicle is approximately 2.35 miles per gallon.

It's worth noting that the mileage rating of a hybrid vehicle can vary depending on factors such as driving conditions and habits, so the actual gas mileage may differ from the stated rating. Additionally, the conversion factors used here are approximate, so the exact gas mileage may vary slightly depending on the specific conversion factors used.

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The probability of obtaining at least one 3 or one 4 when rolling two fair dice can be calculated using complementary probability. First, find the probability of not rolling a 3 or 4 on each die, and then use this to determine the probability of the desired outcome.

For a single die, the probability of rolling a 3 or 4 is 2/6 (since there are 2 favorable outcomes out of 6 possible outcomes).

Therefore, the probability of not rolling a 3 or 4 on one die is 1 - 2/6 = 4/6 or 2/3.

When rolling two dice, the probability of not rolling a 3 or 4 on both dice is the product of their individual probabilities, which is (2/3) * (2/3) = 4/9.

Now, to find the probability of obtaining at least one 3 or one 4, we use the complementary probability:

Probability(at least one 3 or one 4) = 1 - Probability(neither die shows 3 or 4) = 1 - 4/9 = 5/9.

So, the probability of obtaining at least one 3 or one 4 when rolling two fair dice is 5/9.

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Probability of

=0.0403.

The probability that exactly two of the 14 students selected with replacement will wear wrist watches is 3/30 * 2/29 * 27/28 * 26/27 = 0.0437.

The probability that exactly two of the 14 students selected without replacement will wear wrist watches is 3/30 * 2/29 * 26/28 * 25/27 = 0.0403.

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The domain for n in the arithmetic sequence is the one in the first option:

all integers where n ≥1

We have a arithmetic sequence defined by the general formula:

aₙ  = 4 - 3*(n - 1)

And we want to find the domain for the possible values of n that we can use in that formula.

Remember that the terms of a sequence are defined as:

a₁, a₂, a₃,...

So the values of n are positive whole numbers, in this case the first one is n = 1.

a₁ = 4 + 3*(1 - 1)

a₁ = 4

And then we can keep using any positive integer, then the correct option is:

all integers where n ≥1

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Answer:10root6

Step-by-step explanation:

The information indicates that the correct answer is 9.76% annually.

The area of mathematics that deals with the characteristics of surrounding space, spatial interactions between distinct objects, and the shape of particular items.

It would take 19 years between 1996 and 2015 in all.

We are aware that the equation: gives a geometric mean of a collection of n positive numbers.

GM =  [tex]((x1)(x2)(x3).............)^{1/n}[/tex]

This would provide us with the product of these values' nth roots.

Thus, the following would be the formula indicating rate of rise over time: -

GM =  [tex](value at the end of the period / value at the start of the period)^{1/n} -1[/tex]

[value at the end of the period / value at the start of the period

Value at the conclusion of the time is equal to 241,364,256, hence the statement stands.

The initial value was 40,257,000.

n = 19

Using values, we obtain:

=[tex](241,364,256/40,257,000)^{1/19} -1[/tex]

= (5.995)1/19 - 1

= 0.0976

= 9.76% per year

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p(x)= (x-4)²-(x-6)². ... 4X - 20 = 0 => X = 20/4 => X= 5.

Answer: 126in

Step-by-step explanation:

ftc6yhunum8im

huju7kt6r

5+10=24

g5ghykn

The vertex form of the equation is:

y = a(x - h)² + k, where a = 1, h = 1, and k = -16

It should be noted that to rewrite the equation in vertex form by completing the square, we first need to factor out the coefficient of x²:

y = x² - 2x - 15

y = (x² - 2x + 1) - 16

y = (x - 1)² - 16

Here, the vertex form of the equation is:

y = a(x - h)² + k, where a = 1, h = 1, and k = -16

The key features revealed by both equations are:

Vertex: The vertex of the parabola is (1, -16).

Axis of symmetry: The axis of symmetry is the vertical line x = 1.

Minimum/Maximum: Since the coefficient of x² is positive, the parabola opens upwards, and the vertex represents the minimum point of the graph.

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If the first and last pages of a document must be printed in color, and only two printers can print in color, then there are a total of 4⁹⁹ ways that 100 pages can be assigned for printing to four printers.

The fundamental principle of counting says that if there are p ways to do one thing and q ways to do another thing, then there are p×q ways to do both things. Number of printers that is able to print in color = 2

Number of colors printed by printers = 2

We have to determine the number of ways are there for the 100 pages to be assigned to the four printers. Now, consider there are no restrictions. Let's break this problem into two parts. First, we have to print 2 pages in color and there are only two color printers. So, number of ways to print the first and the last page of the document = 2²

= 4

Number of remaining pages of document = 98

Number of avaliabile printers = 4

Now, second part, we have only 98 pages (out of 100 pages, 2 colors pages are already printed). Each of these 98 pages can be assigned to a printer in 4 ways. So, number of ways to print remaining 98 pages of document = 4⁹⁸.

Using the counting principle, number of ways for printing the 100 pages by four printers = 2² × 4⁹⁸

= 4 × 4⁹⁸ = 4⁹⁹

Hence, required number of ways are 4⁹⁹.

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Yes, this relation is a function and here the domain and range are:

domain = {3,6,2,-7} and range ={0,-2,-1,0}

Domain and Range:

The domain and scope of a function are part of the function. The domain is the set of all input values ​​of a function, and the range is the possible outputs given by the function. Field → Function → Sequence. If there is a function f : A → B such that each element of set A corresponds to an element of set B, then A is the field and B is the codomain. The graph of an element "a" under a relation R is given by "b", where (a,b) ∈ R.

The scope of the function is the set of images. The domain and range of a function are usually expressed as:

Domain(f) = {x ∈ R: State} and range(f)={f(x): x ∈ domain(f)}

According to the Question:

The given function is:

{(3,0),(6,-2),(2,-1),(-7,0)}

It is a function as every input has a single output.

So, 3,6,2,-7 are the elements of the domain of the given relation.

Here domain = {3,6,2,-7} and range ={0,-2,-1,0}

Therefore, this relation is a function.

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